régression linéaire
# Implementation of gradient descent in linear regression
import numpy as np
import matplotlib.pyplot as plt
class Linear_Regression:
def __init__(self, X, Y):
self.X = X
self.Y = Y
self.b = [0, 0]
def update_coeffs(self, learning_rate):
Y_pred = self.predict()
Y = self.Y
m = len(Y)
self.b[0] = self.b[0] - (learning_rate * ((1/m) *
np.sum(Y_pred - Y)))
self.b[1] = self.b[1] - (learning_rate * ((1/m) *
np.sum((Y_pred - Y) * self.X)))
def predict(self, X=[]):
Y_pred = np.array([])
if not X: X = self.X
b = self.b
for x in X:
Y_pred = np.append(Y_pred, b[0] + (b[1] * x))
return Y_pred
def get_current_accuracy(self, Y_pred):
p, e = Y_pred, self.Y
n = len(Y_pred)
return 1-sum(
[
abs(p[i]-e[i])/e[i]
for i in range(n)
if e[i] != 0]
)/n
#def predict(self, b, yi):
def compute_cost(self, Y_pred):
m = len(self.Y)
J = (1 / 2*m) * (np.sum(Y_pred - self.Y)**2)
return J
def plot_best_fit(self, Y_pred, fig):
f = plt.figure(fig)
plt.scatter(self.X, self.Y, color='b')
plt.plot(self.X, Y_pred, color='g')
f.show()
def main():
X = np.array([i for i in range(11)])
Y = np.array([2*i for i in range(11)])
regressor = Linear_Regression(X, Y)
iterations = 0
steps = 100
learning_rate = 0.01
costs = []
#original best-fit line
Y_pred = regressor.predict()
regressor.plot_best_fit(Y_pred, 'Initial Best Fit Line')
while 1:
Y_pred = regressor.predict()
cost = regressor.compute_cost(Y_pred)
costs.append(cost)
regressor.update_coeffs(learning_rate)
iterations += 1
if iterations % steps == 0:
print(iterations, "epochs elapsed")
print("Current accuracy is :",
regressor.get_current_accuracy(Y_pred))
stop = input("Do you want to stop (y/*)??")
if stop == "y":
break
#final best-fit line
regressor.plot_best_fit(Y_pred, 'Final Best Fit Line')
#plot to verify cost function decreases
h = plt.figure('Verification')
plt.plot(range(iterations), costs, color='b')
h.show()
# if user wants to predict using the regressor:
regressor.predict([i for i in range(10)])
if __name__ == '__main__':
main()
Alvin Saini
